Effects of pore size, water content, and oxygen-containing functional groups on oxygen adsorption in bituminous coal

To further explore the mechanism of coal spontaneous combustion and better grasp the laws of spontaneous combustion, this article studied the adsorption behavior of O2 in coal. Materials studio software was applied to study the adsorption of oxygen under different water content, different pore sizes, and different oxygen-containing functional groups by means of grand canonical Monte Carlo and molecular dynamics simulation methods. The results show that the adsorption capacity of O2 decreases with the increase in water content. With the increase of molecular pore size of coal, the adsorption capacity of O2 increases, and the tight adsorption amounts decrease. The equivalent adsorption heat is less than 42 kJ/mol, indicating that the adsorption of O2 in coal pores is physical adsorption. The smaller the physical adsorption energy and charge transfer value of the hydroxyl group for O2, it indicates that the hydroxyl group is the active group for the physical adsorption of O2.


Scientific Reports
| (2023) 13:10373 | https://doi.org/10.1038/s41598-023-37632-w www.nature.com/scientificreports/ etc. To further explore the mechanism of coal spontaneous combustion and better grasp the law of spontaneous combustion, we should increase the research on coal oxygen adsorption. In this paper, the process of coal physical adsorption of oxygen will be numerically simulated, analyze the relevant factors affecting coal oxygen adsorption, get the law of coal physical adsorption of oxygen, to provide theoretical support for the determination of coal spontaneous combustion, so as to better prevent accidents caused by coal spontaneous combustion.

Methods
Model construction and optimization. The molecular structure model of bituminous coal proposed by Li was adopted in this study 19 , whose molecular formula is C 174 H 148 O 5 N 2 .
In order to obtain a relatively stable adsorbent structure model, this study carried out geometric optimization of coal molecular monolith under the Forcite module. The selection of the force field is very important in simulation calculation. In setting the force field, the Universal force field (UFF) was used. Compared with the Dreiding force field adopted by Sun et al. 20 , UFF includes all elements in the periodic table and can specify a method for charge calculation with high calculation accuracy. Smart flexible optimization method was adopted. The convergence mass deviation was set to Ultra-fine, the value 0.001 kcal/mol, the RMS Force 0.1 kcal/mol, and the RMS Displacement was set to 0.03 Å. The charge balance method was adopted for charge calculation, the cutoff radius was 4.5 Å, buffer width was 0.5 Å. Atom-Based van der Waals action was adopted, electrostatic action was the Ewald method, and the number of iterative calculation steps was set to 5000 21,22 . The stable configuration of the coal molecular cell obtained after the repeated iterative calculation is shown in Fig. 1.
After it obtained the constructed coal macromolecular models, it used the Forcite module to optimize the system at the steepest descent, eliminating overlapping conformations, and setting the maximum iterative steps, force field, charge, electrostatic, and van der Waals parameters as well as those specified in the optimization. Finally, the model of coal macromolecular surface adsorbent was optimized. In addition, the energy comparison before and after optimization of the model structure in Table 1 shows that the overall energy of the model decreases, indicating that the overall structure of the model tends to be stable and the stable configuration is finally obtained.
Adsorption simulation parameter settings. The GCMC method is used for adsorption simulation calculation, which is mainly used to solve the problem of molecular random diffusion, and is widely used in materials, chemistry, and physics 23 .
It is assumed that the molecular model of coal does not deform during the adsorption process and the layer spacing is unchanged. The adsorption of O 2 was calculated under the Sorption module. Fixed pressure was selected for the task, and the Metropolis method was adopted. The simulated balance steps and process steps were both set as 1.5 × 10 6 steps, the fixed pressure was 101 kPa, and the force field was the universal force field (UFF). The charge balance method (Qeq) was used for the charge, the Atom-Based van der Waals interaction  www.nature.com/scientificreports/ was used, and the Ewald method was used for electrostatic interaction. The simulated adsorption calculation was carried out at a temperature of 298 K.
Parameter setting of molecular dynamics simulation. After completing the adsorption calculation of the model, MD should be used to study the motion trajectories of molecules in the system, through which the adsorption concentration data can be obtained. The lowest energy configuration returned was selected, and the Dynamics task was selected under the Forcite module. The canonical ensemble (NVT) was used for simulation calculation, and the temperature corresponding to the adsorption temperature was selected respectively. The time step of the simulation was set as 1 fs, the total number of steps was 1 × 10 6 , and the total simulation time was 1000 ps. Other parameters were set with the adsorption simulation parameters. When researching the effect of water content on coal Adsorption of oxygen molecules, the first time to determine the adsorption position of water molecules in coal macromolecular structure model was using the adsorption module. After adding water molecules to the model, structural optimization and MD simulation need to be carried out again.
Density functional theory. Density functional theory (DFT) calculation of the adsorption of different functional groups in coal molecules is carried out in the CASTEP (Cambridge sequential total energy package) module of MS software 24 . The exchange-correlation function for geometric optimization of different functional group structures uses the GGA-PWE function and the OBS method of PW91 functional (for dispersion correction), and the plane wave truncation energy is set to 400 eV 25 .

Results and discussion
Influence of moisture content on adsorption of O 2 . In this research, the O 2 adsorption capacity of the coal structure model is calculated when the temperature is 298 K, the pressure is 101 kPa, and the water content is 0%, 0.5%, 1%, 2%, 3%, and 4% respectively. Corresponding to 0, 3, 5, 8, and 10 water molecules were added to the coal molecules. Figure 2 is the initial and final states of the water-coal system and the water-coal-oxygen system. The formula for calculating water content is as follows: where M H2O is the molecular mass of water, g/mol; M coal is the molecular mass of coal, g/mol; W is water content, %.
When analyzing the influence of water content on gas adsorption capacity, the water content in coal is set as 0%, 0.5%, 1%, 2%, 3%, and 4% respectively. The relationship between oxygen adsorption capacity and water content is shown in Fig. 3. It can be seen from the figure that oxygen adsorption capacity decreases with the The initial and final states of the water-coal system and the water-coal-oxygen system. In the range of 0-4% water content, the adsorption capacity of O 2 decreased from 21.54 mmol/g at 0% water content to 14.82 mmol/g at 4% water content. Water molecules are polar molecules. When dry coal is in contact with moist air, water molecules will react with oxygen-containing free radicals on the surface of coal to form chemically bound water. The free radical-oxygen-carbohydrate generated by the reaction promotes the formation of water and provides more active sites for the adsorption of coal and oxygen. The greater the amount of oxygen adsorbed by coal, the more water molecules in the air can promote the oxygen adsorption of coal at this stage. However, with the increasing water content, when all oxygen-containing functional groups are occupied, the excess water molecules begin to adsorb on the pore surface of coal in the form of free water and keep condensing, and finally form water-containing liquid film on the pore surface, hindering the diffusion and adsorption of oxygen 26 . Influence of pore size on oxygen adsorption. Coal is a porous medium consisting mainly of micropores and mesoporous. The micropore size is less than 2 nm and the mesopore size is between 2 and 50 nm. The adsorption behavior mainly occurred in micropores and mesoporous pores, while the diffusion behavior mainly occurred in mesoporous pores 27 . Figure 4 shows a model of the five types of pores.
As shown in Fig. 5, with the increase of the molecular pore size of coal, the adsorption capacity of gas also increases. This suggests that the larger the pore size, the more molecules of coal and gas can be accommodated in the pores. The adsorption heat of O 2 ranges from 7 to 10 kJ/mol and is less than 42 kJ/mol, indicating that the adsorption of O 2 in coal pores is physical adsorption 28 .
By analyzing the concentration of gas molecules in different pore models, the distribution of gas molecules in the coal molecular layer and pores can be obtained, as shown in Fig. 6. When the pore size is 0.5 nm, the adsorption rate of O 2 in the pore is 9.2%. It can be found that the concentration distribution of gas in the pore is proportional to the pore size.
The tight gas adsorption capacity of different pore models is shown in Fig. 7. The adsorption capacity of tight gas in different pore models decreases with the increase of pore size. In the 0.5 nm pore model, the adsorption capacity of O 2 was 19.18 mmol/g. In the 5 nm pore model, the adsorption capacity of O 2 is 17.55 mmol/g, which is 8.5% lower than that in the 0.5 nm pore model. In micropores, the distance between adjacent coal molecular layers is very small, so the coal molecular layer in micropores exerts greater force on gas molecules than the coal molecular layer in mesoporous pores. Therefore, the adsorption of gas molecules in coal molecules decreases with the increase of pore size. With the decrease in pore size, the number of pores exposed to air increased, and the oxygen adsorption capacity increased.
The diffusion characteristics of gases with different pore sizes were studied. Through MD simulation, the relationship between the root mean square displacement (MSD) of the gas in the pore model and simulation time was obtained, as shown in Fig. 8.
The diffusion coefficient in Fig. 9 was obtained from the slope in Fig. 8. As shown in Fig. 9, the diffusion coefficient of the gas increases with the increase of the aperture. The diffusion coefficient of O 2 increases from 3.98 × 10 −8 to 9.85 × 10 −8 m 2 /s. With the change of pore size, the gas diffusion in microporous structure is obviously weaker than that in mesoporous structure. In the effective cutoff radius (1.25 nm), gas molecules are more affected by van der Waals forces in the pore. In contrast, when the atomic spacing exceeds 1.25 nm, the effects of van der Waals forces and electrostatic forces are weakened and the diffusion of gas molecules through pores is enhanced 29 .   In the formula, E coal/gas is the total energy of coal adsorbed gas molecules; E coal and E gas are the energies of coal and gas molecules, respectively. According to this definition, E ads is a negative value and represents exothermic adsorption. The larger the absolute value, the stronger the adsorption.
The physical adsorption parameters of O 2 molecule are listed in Table 2. It can be seen that hydroxyl and ether bonds have lower physical adsorption energy values, and they have higher physical adsorption capacity for O 2 molecules. The physical adsorption equilibrium distance between hydroxyl group and O 2 is relatively small, while the physical adsorption distance between other adsorption sites and O 2 is greater than 3 Å. Milliken charge transfer represents the degree of polarization of O 2 in physical adsorption, with the hydroxyl group having a higher charge, followed by the carbonyl group and ether bond, indicating that O 2 is adsorped more stably near these adsorption sites. During the adsorption process, the smaller the physical adsorption energy and charge transfer (2) E ads = E coal/gas − E coal − E gas

Conclusion
MS software was applied to study the adsorption of oxygen under different water content, different pore sizes, and different oxygen-containing functional groups by means of GCMC and MD simulation methods. The conclusions are as follows: (1) With the increase in water content, oxygen adsorption capacity decreases. Water molecules gather on the pore surface of coal to form a water film, which hinders the transport and adsorption of oxygen and reduces the amount of oxygen adsorption. (2) The pore size of coal also affects the adsorption capacity of oxygen, and as the pore size of coal molecules increases, the adsorption capacity of O 2 increases. However, the dense adsorption capacity decreases with the increase in pore size. The adsorption heat of equal amounts is less than 42 kJ/mol, indicating that the adsorption of O 2 in coal pores is physical adsorption. (3) Due to the minimum physical adsorption energy and charge transfer value of hydroxyl on O 2 , it indicates that hydroxyl is the active group for the physical adsorption of O 2 . (4) One of the physical adsorption functions of coal spontaneous combustion is to transport oxygen for oxidation reaction. The study of the influencing factors in the process of low-temperature oxidation can provide theoretical basis for the analysis of the process of low-temperature oxidation of coal and the prevention and control of spontaneous combustion of coal. In the future, on the basis of this research, we will study inert gases, inhibitors and other fireproof materials to reduce the physical adsorption of coal oxygen, more effectively reduce the low-temperature oxidation of coal and the occurrence of coal fire.

Data availability
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.